2024 Spring Course Syllabus - Mathematics 5032.001

Course: Mathematics 5032.001.

Course Title: Stochastic Calculus.

Credits: 3.

How this course will be taught: In-person.

Time: Tuesdays and Thursdays 12:30-1:50 p.m.

Place: Wachman 617.

Instructor: Atilla Yilmaz.

Instructor Office: Wachman 612.

Instructor Email: atilla.yilmaz@temple.edu

Instructor Phone: -.

Course Web Page: Please check Canvas regularly for announcements, exam dates, homework, numerical projects, etc

Office Hours: TBA.

Prerequisites: MATH 2043 (Calculus III, i.e., multivariable calculus), MATH 2101 (Linear Algebra), MATH 3031 (Probability Theory I), or equivalent. Prior knowledge of basic stochastic processes or advanced calculus (i.e., mathematical analysis) can be helpful but is not assumed.

Course Materials: L.-P. Arguin, A First Course in Stochastic Calculus, Pure Appl. Undergrad. Texts, 53, AMS, 2022.

Course Goals: To introduce the theory of Ito calculus and stochastic differential equations based on Brownian motion and Gaussian processes (avoiding concepts and results from measure theory whenever possible); to illustrate the theory with concrete examples and numerical projects; to present the applications of the theory to option pricing in finance.

Topics Covered: Basic notions of probability; Gaussian processes; properties of Brownian motion; Martingales; Ito calculus; multivariate Ito calculus; Ito processes and stochastic differential equations; the Markov property; change of probability; applications to mathematical finance.

Course Grading: Homework (weekly) 20%; numerical projects (weekly) 20%; midterm exam 25%; final exam 35%.

Exam Dates: The date of the midterm exam will be announced at least two weeks in advance. The final exam will be during the week officially designated by the University. Both exams will be in-class and closed-book.

Attendance Policy: -.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Homework: A problem set will be assigned after the last lecture of each week (on Canvas), due right before the last lecture of the following week (in person). Late homework will not be accepted. At the end of the semester, the lowest homework score of each student will be dropped.

Numerical projects: Small numerical projects will be assigned every week (on Canvas). Students will write the code in Python in a Jupyter notebook. The coding is elementary and the necessary Python knowledge can be picked up along the way.

Make-up: An excused absence for the midterm or the final exam requires notification in advance, followed by valid documentation. Otherwise, the student will receive "0" for any missed exam.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

AI Policy: The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.